@benny.math: Most people learn ad − bc as a formula to memorize. It's actually a measurement. Take the matrix [[3,1],[1,2]]. Read its columns as two vectors, (3,1) and (1,2), drawn from the origin. Complete the parallelogram they span. The determinant, 3·2 − 1·1 = 5, is exactly the area of that parallelogram — five grid squares, countable one by one. The same logic carries into three dimensions. Three column vectors span a slanted box, and the 3x3 determinant gives its volume. In the video the box gets sheared sideways and the number doesn't budge, because tilting a shape doesn't change how much space it occupies. Seen this way, a determinant is a stretch factor: it tells you how much a transformation inflates or shrinks space. And a determinant of zero means the shape has been flattened to nothing — which is the real reason those matrices have no inverse. Follow Benny Math for more visual explanations of the formulas nobody explained properly the first time. #math #linearalgebra #determinant #education #bennymath

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Saturday 31 October 2026 18:33:11 GMT